Suppose that W1, W2, ..., Wm and Vare all finite dimensional vector spaces over F. Prove thatL(V,W1 × ·...x Wm) and L(V, W1) × · x L(V, Wm) are isomorphic vector spaces.

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Answered: Suppose that W1, W2,. , Wm and V are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that W1, W2,. , Wm and V are all finite dimensional vector spaces over F. Prove that 2,... L(V,W1 x ·…× Wm) and L(V, W1) × … .× L(V, Wm) are isomorphic vector spaces.